Effective higher-order nonlinear coefficients of composites with weakly nonlinear media

The field equations, based on the third-order perturbation expansion of electrostatic potential, are derived, and our general formulae for higher-order effective nonlinear coefficients based on the energy definition, are presented and applied to dielectric composites consisting of dilute linear cylindrical inclusions randomly dispersed in a weakly nonlinear host media. The effective nonlinear coefficients are determined up to the ninth order. In addition, the results are also compared to those obtained using the average field method and likely to provide more accurate predictions of effective higher-order nonlinear responses.